River Water Velocity (Shortest Path) – Rankers Physics

Uncategorized: Practice Problem & Solution

The speed of a boat is \(5 text{ km/hr}text{ in still water. It crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of river water is: (1998)}\
\(3 text{ km/hr}\)
\(4 text{ km/hr}\)
\(5 text{ km/hr}\)
\(2 text{ km/hr}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Relative velocity for crossing a river along the shortest path.
Formula: \(v_g = d/t\), \(v_b^2 = v_g^2 + v_r^2\).
Resultant velocity \(v_g = (1text{ km}) / (1/4text{ h}) = 4text{ km/h}\).
Using \(v_b^2 = v_g^2 + v_r^2\), we get \(5^2 = 4^2 + v_r^2\).
So, \(v_r = sqrt{25 - 16} = sqrt{9} = 3text{ km/h}\).

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